On a partial converse of the Montessus de Ballore theorem in \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: On a partial converse of the Montessus de Ballore theorem in \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0533.41012
DOI: 10.1016/0021-9045(84)90063-7
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: The paper is divided into three sections, namely, {\S}1 Introduction, {\S}2 Notation, definitions and some properties, {\S}3 Convergence. The introduction provides some motivation for the paper, while the next section develops notation, presents definitions and discusses results pertaining to certain algebraic properties. The section on convergence carries the main results of this paper. These are theorems 3.1 and 3.2 which are respectively the Montessus de Ballore theorem and its partial converse. The algebraic properties of the unisolvent rational approximants presented by theorems 2.1, 2.2 and 2.3, are restatements of results due to the author [J. Math. Anal. Appl. 53, 89-98 (1976; Zbl 0319.32005)]. Theorem 3.1, as stated in this paper, is perhaps sharper than what appeared in another paper without proof [Approximation Theory III, Proc. Conf. Hon. G. G. Lorentz, Austin/Tex. 1980, 603-609 (1980; Zbl 0481.41014)]. The new result of the paper is the theorem 3.2. This theorem, even though it is not an exact converse of theorem 3.1, indicates clearly that under less stringent set of conditions, one can still recover the meromorphicity of the function f over \(\Delta^ n\!_{\rho}\).
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 3846139
zbMATH Keywords: unisolvent rational approximant
zbMATH Keywords: meromorphicity
zbMATH Keywords: Montessus de Ballore theorem
author: Clement H. Lutterodt
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90063-7
OpenAlex ID: W2047074995
cites work: Q4161937
cites work: Q3937811
cites work: Inequalities expressing degree of convergence of rational functions
cites work: Q5515607
cites work: Rational approximants to holomorphic functions in \(n\)-dimensions
description: scientific article; zbMATH DE number 3846139